How can I use an AutoNum field but suppress the period after the number or
use a different separator character?

You can't use the AutoNum field for this (at least, not on the PC), but you
can
achieve this using the AutoNumLgl field:

1. Select Insert + Field.

2. On the
“General Switches”
tab, you can use the
Add button if you want to add switches that make the number appear
in alphabetic or roman formats

3. On the
“Field-specific switches”
tab, you can use the
Add button if you want to add switches to suppress the trailing
period (\e) or to convert the period to a different separator
character (\s, followed by the separator character you want in
quotes)

So, for example, the field to create an auto-numbered list with no separator,
such as
1 Some text
2 Some text
would be:

{ AUTONUMLGL \e }

The field to create an alphabetically numbered list using a bracket
separator:
a) Some text
b) Some text
would be:

{ AUTONUMLGL \* alphabetic \s ")" }

The braces in the examples above ({ }) do not represent text;
they represent the field braces that are inserted automatically when you use the
Insert + Field dialog. You can also insert them using Ctrl+F9 if
you want to create the field without using the dialog.

Note that using the AutoNumLgl field with built-in Heading styles – provided
you use Arabic numbering (the default) – allows you to create an outline
list in Legal style if you want to. For instance, using the \e switch, you can
create a list of type.: 1 This is a Heading 1 paragraph
1.1 This is a Heading 2 paragraph
2 This is a Heading 1 paragraph

or even of type: 1 This is a Heading 1 paragraph
1.1 This is a body text paragraph
2 This is a Heading 1 paragraph

However, you can nevertheless use the field to create simple lists, and doing
so gives you far more flexibility than using the AutoNum field, due to the
number of switches supported by AutoNumLgl.